Computing apparatus of the neural network type has been described, for instance, by J. J. Hopfield in "Neurons With Graded Response Have Collective Computational Properties Like Those of Two-state Neurons"; Proc. Natl. Acad. Sci., USA Vol 81, pp. 3088-3092 (1984) and by J. J. Hopfield and D. W. Tank in "Neural Computation of Decisions in Optimization Problems", Biological Cybernetics, Vol. 52, (1985), 141-152; as well as in U.S. Pat. No. 4,660,166 dated Apr. 21, 1987 to J. J. Hopfield and U.S. Pat. No. 4,719,591 dated Jan. 12, 1988 to J. J. Hopfield and D. W. Tank. For a general discussion of the mathematical physics used in the present invention, reference is made to H. Goldstein, Classical Mechanics, 2.sup.nd edition, Addison-Wesley, Reading, Massachusetts, 1980, 672 ff and to D. Laugwitz, Differential and Riemannian Geometry, Academic Press, New York, 1965, 238 ff.
Previous networks, such as the Hopfield network as described in J. J. Hopfield, "Neural Networks and Physical Systems With Emergent Collective Computational Abilities", Proc. Natl. Acad. Sci., U.S.A., Vol 79, p. 2554(1982); J. J. Hopfield, "Neurons With Graded Response Have Collective Computational Properties Like Those of a Two-State Neuron" Proc. Natl. Acad. Sci., U.S.A. Vol. 81, p. 3088 (1984); and J. J. Hopfield and D. W. Tank, "Computing With Neural Circuits: A Model", Science, Vol. 233, p. 625(1986) minimize a system Hamiltonian EQU H=T+V (1)
to find local and global minima. These networks have been applied to feature extraction, associative recall, and constraint satisfaction (or problem optimization). Problems associated with use of these networks include convergence on a local minimum and not the global minimum, giving rise to non-optimal solutions.
A number of electronic neural network architectures of the Hopfield type have also been described in the literature: L. D. Jackel, H. P. Graf, and R. E. Howard in "Electronic Neural Network Chips", Applied Optics, Vol. 26, p. 5077 (1987); A. P. Thakoor, A. Moopen, J. Lambe, and S. K. Khanna in "Electronic hardware implementation of neural networks", Applied Optics, Vol. 26, p. 5085 (1987); D. B. Schwartz, R. E. Howard, J. S. Denker, R. W. Epworth, H. P. Graf, W. Hubbard, L. D. Jackel, B. Straughn, and D. M. Tennant, Appl. Phys. Lett., Vol. 50, p. 16 (1987); and L. D. Jackel, R. E. Howard, H. P. Graf, B. Straughn, and J. S. Denker, J. Vac. Sci. Tech., Vol. B4, p. 61 (1986). The following references herein cited contain features which can be incorporated and used with the present invention and are therefore incorporated herein by reference in their entireties.